# K-epsilon models

(Difference between revisions)
 Revision as of 09:14, 15 May 2008 (view source) (→Introduction)← Older edit Latest revision as of 16:03, 18 June 2011 (view source) (→References) (4 intermediate revisions not shown) Line 2: Line 2: == Introduction == == Introduction == - The K-epsilon model is one of the most common [[Turbulence modeling|turbulence models]]. It is a [[Two equation models|two equation model]], that means, it includes two extra transport equations to represent the turbulent properties of the flow. This allows a two equation model to account for history effects like convection and diffusion of turbulent energy. + The K-epsilon model is one of the most common [[Turbulence modeling|turbulence models]], although it just doesn't perform well in cases of large adverse pressure gradients (Reference 4). It is a [[Two equation models|two equation model]], that means, it includes two extra transport equations to represent the turbulent properties of the flow. This allows a two equation model to account for history effects like convection and diffusion of turbulent energy. The first transported variable is turbulent kinetic energy, $k$.  The second transported variable in this case is the turbulent dissipation, $\epsilon$. It is the variable that determines the scale of the turbulence, whereas the first variable, $k$, determines the energy in the turbulence. The first transported variable is turbulent kinetic energy, $k$.  The second transported variable in this case is the turbulent dissipation, $\epsilon$. It is the variable that determines the scale of the turbulence, whereas the first variable, $k$, determines the energy in the turbulence. - To calculate boundary conditions for a calculation using this model see [[Turbulence free-stream boundary conditions|turbulence free-stream boundary conditions]]. + There are two major formulations of K-epsilon models (see [[#References|References]] 2 and 3).  That of Launder and Sharma is typically called the [[Standard k-epsilon model | "Standard" K-epsilon Model]].  The original impetus for the K-epsilon model was to improve the mixing-length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows. + + As described in [[#References|Reference]] 1, the K-epsilon model has been shown to be useful for free-shear layer flows with relatively small pressure gradients.  Similarly, for wall-bounded and internal flows, the model gives good results only in cases where mean pressure gradients are small; accuracy has been shown experimentally to be reduced for flows containing large adverse pressure gradients.  One might infer then, that the K-epsilon model would be an inappropriate choice for problems such as inlets and compressors. + + To calculate boundary conditions for these models see [[Turbulence free-stream boundary conditions|turbulence free-stream boundary conditions]]. == Usual K-epsilon models == == Usual K-epsilon models == Line 15: Line 19: == Miscellaneous == == Miscellaneous == # [[Near-wall treatment for k-epsilon models]] # [[Near-wall treatment for k-epsilon models]] + + ==References== + [1] {{reference-paper|author=Bardina, J.E., Huang, P.G., Coakley, T.J.|year=1997|title=Turbulence Modeling Validation, Testing, and Development|rest=NASA Technical Memorandum 110446}} + + [2] {{reference-paper|author=Jones, W. P., and Launder, B. E.|year=1972|title=The Prediction of Laminarization with a Two-Equation Model of + Turbulence|rest= International Journal of Heat and Mass Transfer, vol. 15, 1972, pp. 301-314}} + + [3] {{reference-paper|author=Launder, B. E., and Sharma, B. I.|year=1974|title=Application of the Energy Dissipation Model of Turbulence to + the Calculation of Flow Near a Spinning Disc|rest=Letters in Heat and Mass Transfer, vol. 1, no. 2, pp. 131-138}} + + [4] '''Wilcox, David C (1998)'''. "Turbulence Modeling for CFD". Second edition. Anaheim: DCW Industries, 1998. pp. 174. [[Category:Turbulence models]] [[Category:Turbulence models]] {{stub}} {{stub}}

## Introduction

The K-epsilon model is one of the most common turbulence models, although it just doesn't perform well in cases of large adverse pressure gradients (Reference 4). It is a two equation model, that means, it includes two extra transport equations to represent the turbulent properties of the flow. This allows a two equation model to account for history effects like convection and diffusion of turbulent energy.

The first transported variable is turbulent kinetic energy, $k$. The second transported variable in this case is the turbulent dissipation, $\epsilon$. It is the variable that determines the scale of the turbulence, whereas the first variable, $k$, determines the energy in the turbulence.

There are two major formulations of K-epsilon models (see References 2 and 3). That of Launder and Sharma is typically called the "Standard" K-epsilon Model. The original impetus for the K-epsilon model was to improve the mixing-length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows.

As described in Reference 1, the K-epsilon model has been shown to be useful for free-shear layer flows with relatively small pressure gradients. Similarly, for wall-bounded and internal flows, the model gives good results only in cases where mean pressure gradients are small; accuracy has been shown experimentally to be reduced for flows containing large adverse pressure gradients. One might infer then, that the K-epsilon model would be an inappropriate choice for problems such as inlets and compressors.

To calculate boundary conditions for these models see turbulence free-stream boundary conditions.

## Miscellaneous

1. Near-wall treatment for k-epsilon models

## References

[1] Bardina, J.E., Huang, P.G., Coakley, T.J. (1997), "Turbulence Modeling Validation, Testing, and Development", NASA Technical Memorandum 110446.

[2] Jones, W. P., and Launder, B. E. (1972), "The Prediction of Laminarization with a Two-Equation Model of Turbulence", International Journal of Heat and Mass Transfer, vol. 15, 1972, pp. 301-314.

[3] Launder, B. E., and Sharma, B. I. (1974), "Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc", Letters in Heat and Mass Transfer, vol. 1, no. 2, pp. 131-138.

[4] Wilcox, David C (1998). "Turbulence Modeling for CFD". Second edition. Anaheim: DCW Industries, 1998. pp. 174.